1. Field of the Invention
The present invention relates generally to the power flow analysis of a power grid embedded with a generalized power flow controller in the technical field and, more particularly, to a method to incorporate the steady-state model of a generalized power flow controller into a conventional Newton-Raphson power flow algorithm, which can be applied to calculate the power flow solution of a power grid embedded with the generalized power flow controller.
2. Description of Related Art
In the last decade, the power industry has extensively employed an innovative Flexible Alternative Current Transmission System (FACTS) technology to improve the utilization of existing transmission facilities. Connecting several Voltage Sourced Converters (VSCs) together forms various multiple functional FACTS controllers, such as: Static Synchronous Compensator (STATCOM) 103, Unified Power Flow Controller (UPFC) 102, and Generalized Unified Power Flow Controller (GUPFC) 101.
The STATCOM, as shown in FIG. 1, has one shunt VSC. The AC side of the shunt VSC connects to a bus of a power grid through a coupling transformer, and the DC side connects to a capacitor. The STATCOM provides reactive power compensation to regulate the voltage magnitude of the connected bus at a fix level.
The UPFC 102, as shown in FIG. 2, has one shunt VSC and one series VSC. The AC side of the shunt VSC connects to a bus through a shunt coupling transformer, whereas the AC side of the series VSC is in series with a transmission line through a series coupling transformer. The DC sides of the shunt and series VSCs share the same capacitor. The shunt VSC can regulate the voltage magnitude of the connected bus at a fixed level, and the series VSC can control the active and reactive power of the connected transmission line.
The GUPFC 101, as shown in FIG. 3, comprises one shunt VSC and a plurality of series VSCs. The connections and functions of the VSCs of the GUPFC 101 are like those in the UPFC 102. These VSCs enable the GUPFC 101 to control the voltage magnitude of the bus connected with the shunt VSC and to control the active and reactive power of each transmission line which is in series with the series VSC.
The disclosed generalized power flow controller has a more flexible structure than the GUPFC 101. Comparing FIG. 3 and FIG. 4, both the GUPFC 101 and the generalized power flow controller have one shunt branch and a plurality of series branches. In the GUPFC 101, the shunt branch and the receiving-end of each series branch connect to a common bus, bus s1. However, in the disclosed generalized power flow controller, the shunt branch and the receiving-end of each series branch are allowed to connect to different buses, bus s1, bus s2˜sn, respectively.
The versatility of the generalized power flow controller can be applied to equalize both the active and reactive power in the transmission lines, to relieve the overloaded transmission lines from the burden of reactive power flow, and to restore for declines in resistive as well as reactive voltage drops.
Developing a steady-state model of the generalized power flow controller is fundamentally important for a power flow analysis of a power grid embedded with the generalized power flow controller. The power flow analysis provides the information of impacts on a power system after installing the generalized power flow controller. Many steady-state models of STATCOM 103, UPFC 102 and GUPFC 101 applied to power flow analysis have been set forth. In 2000, a STATCOM 103 steady-state model accounting for the high-frequency effects and power electronic losses is proposed in an article “An improved StatCom model for power flow analysis”, by Zhiping Yang; Chen Shen; Crow, M. L.; Lingli Zhang; in IEEE Power Engineering Society Summer Meeting, 2000, Volume 2, Page(s):1121-1126.
A conventional approach to calculate the power flow solution of a power grid that includes a unified power flow controller is disclosed in an article “Unified power flow controller: a critical comparison of Newton-Raphson UPFC algorithms in power flow studies” by C. R. Fuerte-Esquivel and E. Acha in IEE Proc. Generation, Transmission & Distribution, 1997, and in an article “A comprehensive Newton-Raphson UPFC model for the quadratic power flow solution of practical power network” by C. R. Fuerte-Esquivel, E. Acha and H. Ambriz-Perez in IEEE Trans. Power System, 2000. In 2003, X.-P. Zhang developed a method to incorporate a voltage sourced based model of the GUPFC 101 into a Newton-Raphson power flow algorithm in an article “Modeling of the interline power flow controller and the generalized unified power flow controller in Newton power flow”, IEE Proceedings. Generation, Transmission & Distribution, Vol. 150, No. 3, May, 2003, pp. 268-274. The method included the voltage magnitude and phase angle of the equivalent voltage source into the state vector of Newton-Raphson iteration formula. The number of appended state variables is twice the number of VSCs. Thus, the length of the state vector is varied depending on the number of VSCs. Therefore, the prior art can only be applied to the case with a fixed number of VSCs. It can not be extended to the applications of STATCOM 103 and UPFC 102. Besides, the speed of convergence is sensitive to the initial values of the control variables of the GUPFC 101. The initial values of the control variables need a careful selection. Improper selection of the control variables may cause the solutions oscillating or even being divergent.
Although the steady-state models of STATCOM 103, UPFC 102 and GUPFC 101 have been widely discussed individually, a method to incorporate steady-state models of STATCOM 103, UPFC 102, GUPFC 101 and the generalized power flow controller into a Newton-Raphson power flow algorithm in a single framework have not been disclosed.